Mathematical Mollusks

To me it’s always incredibly amazing and beautiful when something rooted firmly in mathematics shows up in nature. When that mathematical entity is also incredibly obscure and complex it gets even better. The two images above show similar (but not quite identical) patterns, one is known as Rule 30 while the other is the pattern on the shell of Conus textile, a marine gastropod. Rule 30 is a cellular automaton which is a mathematical tool used to see the change in a system over time. In these a cell can exist in several states dependent on certain variables, in rule 30 there are two states a cell can be in that is determined by the state of adjacent cells. Over time rows are added and a pattern begins to emerge that exhibits chaotic behavior. A similar pattern can also be seen here on the shell of C. textile, a venomous marine gastropod.